Equivalent Circuit Model for Tantalum and Niobium Oxide Capacitors for us in Simulation Software

EQUIVALENT CIRCUIT MODEL FOR TANTALUM AND NIOBIUM
OXIDE CAPACITORS FOR USE IN SIMULATION SOFTWARE
J. Pelcak
AVX Czech Republic s.r.o., Dvorakova 328, 563 01 Lanskroun, Czech Republic
Phone: +420 465 358 127 Fax: +420 465 358 128, email pelcakj@avx.cz
ABSTRACT
0
R16
In electrical circuit simulations with simulation
software, ideal passive components (resistors,
capacitors, inductors) are typically used because
real component characteristics have been difficult
to model. Unfortunately, ideal and real passive
components have significant differences in their
electrical behavior. These differences lead to
discrepancies between actual hardware performance
and expected results based upon simulation
software programs.
This paper will describe the development of
equivalent circuit diagram for modeling real
capacitor behavior. Use of this real model in
simulation software can help make circuit
development more efficient, as the circuits in the
simulations should have similar behavior to the
actual circuits.
The model presented here includes real component
behavior for Tantalum and Niobium Oxide
capacitors, with all factors such as ESR and
inductance, and even includes the dependence on
temperature.
INTRODUCTION
All real components including capacitors have
parasitic factors not taken into account in ideal
models. These factors can have a major impact on
electrical behavior within a circuit. Better
understanding of real capacitor behavior can help to
create more accurate solutions for circuit
development. The use of an equivalent circuit that
accurately represents the true behavior of a
capacitor will yield a better understanding of
response in the electrical circuit.
COMPARISON
CAPACITORS
OF
IDEAL
AND
REAL
An Ideal capacitor has only a capacitance value,
which does not depend on frequency, temperature,
applied voltage, and has no parasitic equivalent
series resistance (ESR), equivalent series
inductance (ESL), and leakage current (LI).
Real capacitors have a capacitance value that varies
with frequency, temperature and applied voltage,
and also has significant ESR, ESL and LI parasitic
electrical parameters. The magnitude of these
5k
0
R5
5k
R13
100M
Q3
C3
100n
R6
68
6
1 3
15
F
VIN E
R
V
CT
RT
ERRERR+
7
6
1
2
4
5
0
0
9
L1
0.9mH
Q2N3703
R7
150
C
S
O
C_A
E_A
12
11
13
14
C_B
E_B
0
C6
NOJC686K 006R
0
D1
120NQ045
0
C1
TA JA106K016R
R12 +
100M
0
R10
5
+
0
1
0
0
1R1
50k
0
2
R8
2k
T
U
H
S
C1
1n
+
Q4
Q2N3703
U1
CL+
P
DCL- M
N O
G C
8
0
C7
NOJC686K 006R
R2
1
C8
+
L1
0.9mH
C9
+
C11
C10
+
+
SG1524B
0
0
0
0
0
TPSV108K004R0035
TPSV108K004R0035
TPSV108K004R0035
TPSV108K004R0035
C2
+
TPS D107K010R0050
parasitic parameters depends on manufacturing
technology, methods and material systems. The
non-ideal parameters have significant influence on
filtering, smoothing and other functions in
electronic applications.
CHARACTERISITCS
CAPACITOR
OF
A
REAL
For a real capacitor, the capacitance value generally
decreases with increasing frequency due to ESR,
and there is a peak at the resonance frequency
because of parasitic ESL.
The dielectric of a real capacitor is not an ideal
insulator, so there is a leakage current through the
component. Furthermore, Tantalum and Niobium
Oxide capacitors are polar components, and due to
the MIS structure [1] of the capacitor, the leakage
behavior under reverse voltage is similar to a
diode’s VA characteristic - with a sharp knee at
about 10% of rated voltage.
These parameters vary with temperature, which has
a measurable influence on the entire circuit
behavior, especially for low power applications.
These are some of the reasons that real capacitors
demonstrate significantly different performance
versus ideal capacitors.
Resistor RLI describes leakage current (LI) through
the component, because the value of resistor RLI
represents a linear change in the modeled
capacitor’s leakage current over application voltage
range (figure 4).
EQUIVALENT CIRCUIT DIAGRAM FOR A
REAL CAPACITOR
An equivalent circuit diagram has been developed
from ideal passive and semiconductor components
(C, R, L, and D) to simulate the actual behavior of
Tantalum and Niobium Oxide capacitors. The
equivalent circuit diagram is shown in figure 1.
LLS
S
Leakage current (uA)
RRS
S
1.6
R00
R
C0
C0
R1
R1
R
R22
R5
R5
R
R44
R
R33
+
DRR
D
RRLI
LI
C1
C
1
C22
C
C3
C
3
CC44
C5
C
5
1.2
0.8
0.4
0
RD
R
D
0
1
-
2
3
4
Application voltage (V)
5
6
Figure 1: The structure of equivalent circuit
diagram (independent on temperature)
Figure 4: Leakage current representation in V-A
characteristic
The equivalent circuit consists of a ladder of ideal
resistors R1, R2, R3, R4, R5 and capacitors C1, C2,
C3, C4, C5 to describe decreasing capacitance
(Figure 2) and drop in ESR (Figure 3) with
Equivalent resistance of leakage current could be
easy recalculated trough Ohm’s law RLI=VA/LI
from known application voltage VA and resistance
LI.
Since Tantalum and Niobium Oxide capacitors are
polar components with MIS (Metal Insulator
Semiconductor) structure [1], the electrical
behavior in reverse voltage is different from that
under regular polarization [2]. In the reverse mode,
tantalum and niobium oxide dielectrics are modeled
by a diode DR and resistor RD integrated in the
equivalent circuit diagram. The diode DR has a bend
at approximately 10% of the capacitor’s rated
voltage to describe the real change of capacitor’s VA curve. Serial resistance RD describes the slope of
V-A characteristic after the bend. The diode DR and
serial resistance RD do not have any influence on
leakage current of the capacitor since the diode DR
has negligible current in the diode’s reverse mode.
Detailed view of the reverse voltage behavior is
visible in figure 5.
Capacitance
100
0
-100
100
1000
10000
100000
1000000
frequency (Hz)
Figure 2: Capacitance behavior through the
frequency range
ESR
ESR (Ohm)
10
1
10
0.1
0.01
100
1000
10000
100000
1000000
frequency (Hz)
Figure 3: Reaction of ESR through the frequency
increasing frequency, which is characteristic of
capacitors in general. The increased ESR level at
low frequencies is described by the resistor R0 and
capacitor C0 in parallel combination. The
capacitance C0 is many times higher than nominal
capacitance of the capacitor, because this C0
capacitance represents static electric charge on the
capacitor. Self-inductance of the capacitor is
modeled by the parallel combination of inductance
LS and resistance RS to create a self-resonance
behavior with the rest of circuit capacitance.
Rs should attenuate the peak pulse of the selfresonance cycle.
Reverse current (mA)
Capacitance (uF)
200
8
6
4
2
0
0
0.5
1
1.5
2
Reverse voltage (V)
2.5
3
Figure 5: Reverse mode V-A characteristic
EXPLANATION
OF
TEMPERATURE
DEPENDENT CAPACITOR MODEL
The
equivalent
circuit diagram includes
temperature dependences, even though this is less
significant for Tantalum and Niobium Oxide
capacitors than for other technologies (tantalum
polymer, aluminum polymer, high CV ceramic
components etc.).
There are no voltage dependences included in the
model, since Tantalum and Niobium Oxide
capacitor characteristics are independent of DC bias
voltage.
Real capacitors are temperature dependent and thus
the components from the equivalent circuit are
functions of temperature as is shown in figure 6.
RRS
S
RR0
0(T)
LLS
S
C0C0
(T)
Resistance (MOhm)
30
25
20
15
10
5
0
-60
R1R1
(T)
R2R2
(T)
R3R3
(T)
R4R4
(T)
-20
20
60
100
140
Temperature (°C)
R5R5
(T)
+
DRR
D
RLI
RLI(T)
C1 (T)
C
1
C22(T)
C
C3 (T)
C
3
CC44(T)
C5 (T)
C
5
Figure 8: Temperature dependent value
equivalent RLI over temperature
of
RD (T)
R
D
-
Figure 6: The structure of equivalent circuit
diagram with temperature dependent components
The temperature dependence is accounted for by
making resistor and capacitor values in the model
functions of temperature: (R1(T), R2(T), R3(T),
R4(T), R5(T)) and (C0(T), C1(T), C2(T), C3(T),
C4(T), C5(T)). This mathematical explanation of
temperature behavior can describe capacitance,
ESR and Impedance reaction of the capacitor across
the frequency spectrum. Figure 7 shows the
capacitance and ESR response through temperature
and frequency range.
Capacitance
200
TANTALUM
AND
NIOBIUM
OXIDE
CAPACITOR MODEL LIBRARY USED IN
SIMULATION SOFTWARE
Today, simulation software is a nearly
indispensable tool in efficient and flexible
development and design of electronic equipment.
The equivalent circuit models developed for
Tantalum and Niobium Oxide capacitors have been
assembled into a library for use in this simulation
software. As described above, these models have
been tuned to match the measurements of the actual
components so that the model will yield the same
performance in the simulation circuit as the actual
component would in the real circuit. Figure 9 shows
Temperature -55°C
Capac itanc e (uF)
Capacitance (uF)
Capacitanc e
200
100
Temperature 25°C
0
Temperature 85°C
Temperature 125°C
-100
100
1000
10000
100000
100
0
1000000
frequency (Hz)
-100
ESR
100
10
1000
10000
100000
1000000
100000
1000000
fre que ncy (Hz)
Temperature -55°C
ES R
10
Temperature 85°C
Temperature 125°C
ES R (Ohm )
ESR (Ohm)
Temperature 25°C
1
0.1
0.01
100
1000
10000
100000
1
0.1
1000000
frequency (Hz)
Figure 7: Capacitance and ESR behavior through
the frequency range with temperature dependence
The leakage current of the capacitor is even
logarithmically temperature dependent and this
influence is included in the RLI(T) temperature
function, which means that the temperature is a key
influence on leakage current magnitude. The
leakage current can be transformed to the
RLI(T)=VA/LI(T) by Ohm’s law and its exponential
explanation can looks like the equation (1) below
with detailed graphical view to plot in figure 8.
(1)
RLI (T ) = RLI 25°c ⋅1.39 ⋅ e −0.013⋅T
0.01
100
1000
10000
fre que ncy (Hz)
Figure 9: Matching real measurement and
simulation response of equivalent circuit
how closely the behavior of the capacitor model
matches the actual component.
Each library consists of two files: a netlist file,
which includes a network of ideal components that
represents the equivalent circuit diagram (Figure 6),
including temperature dependences, and a
component symbol file that contains symbols that
represent the components on the circuit diagram.
The libraries contain models for all AVX Tantalum
and Niobium Oxide capacitors, and can be imported
into PSpice and other popular simulation software.
[3].
The next chapter will describe the use of the library
in creating simulation circuits.
These libraries are intended for use in both
frequency and transient simulations over the full
operating temperature range of each component. A
complete designed circuit diagram could be built
from many types of components (transistors,
resistors, capacitors, diodes, inductors, integrated
circuits, etc.). One such circuit diagram is shown in
figure 10.
20u
0
Capacitance
10
1.0
100m
ESR
1.0K
1.0
10Hz
100Hz
1.0KHz
10KHz
Impedance
100KHz
1.0MHz
10MHz
Frequency
Figure 12: Capacitance, ESR and Impedance
behavior of simulated real capacitor
0
R16
5k
R13
100M
C7
NOJC686K006R
16
3
7
6
1
2
8
R4
5k
0
R7
150
12
11
C_A
CT
E_A
RT
ERRERR+ C_B
E_B
CL+
CL-
4
5
0
Q4
Q2N3703
U1
C1
1n
0
+
+
R10
5
Figure 13 shows a circuit diagram used to compare
the level of smoothing given by tantalum and
0
0
C6
NOJC686K006R
R1
0
D1
120NQ045
0
R1
50k
0
R8
2k
13
14
SHUT
R3
5k
COMP
20V
VIN
L1
0.9mH
L1
C1
TAJA226K006R
2
15
Q2N3703
0.5
1
20n
0
R6
68
VREF
OSC
0 C2
TPSD336K025R0200
TPSD336K025R0200
GND
V1
0
Q3
C3
100n
50uH
R2
5
0
10
V2
R5
5k
C4
9
C5
+
0.1
+
R11
+
0
R12
100M
R3
1u
V1
V2 = 5
PER = 1u
PW = 0.5u
0
0
SG1524B
Figure 10: Example of circuit diagram suitable for
simulation
For many practical purposes, the simulation result
can be considered identical to what would be
measured on the physical circuit. And simulation of
the circuit is more efficient and more flexible than
assembling the circuit from real components on a
PCB, which can result in reduced overall time-tomarket.
EXAMPLE
OF
CIRCUIT
DIAGRAM
CREATION WITH SIMULATED AND
MEASURED RESULTS
R4
L2
0.5
50uH
C2
22u_10V_Y5V
R6
5
R5
1u
Figure 13: Circuit diagram of output passive filters
comparison
ceramic capacitors in output passive filters. The
output voltage ripple is shown in figure 14.
2.325V
2.321V
2.318V
2.315V
This section gives examples creating circuit
diagrams, their subsequent simulation, and results.
R1
1
V(tantalu m)
2.316V
2.315V
2.315V
V(ceramic)
5.0V
V1
1V
+
2.5V
C3
TAJA226K004R
0
0
Figure 11: Basic circuit diagram of real capacitor
simulation
Components are basically dragged and dropped
onto the worksheet to create the circuit diagram
(Figure 11). In this example the capacitor is
connected with a sweeping source to demonstrate
frequency response of electrical parameters and
evaluate real capacitance, ESR and impedance
characteristics. The results are shown against
measurement of the actual device in figure 12.
0V
590us
591us
V(input)
V(tantalu m)
V(ceramic)
592us
593us
594us
Time
Figure 14: Simulation result of ripple voltage
In this case, the tantalum capacitor has a smoother
voltage ripple characteristic V(tantalum) than the
ceramic V(ceramic), where voltage spikes are
present, although overall output filtering is similar.
For comparison, the same circuit was assembled
from actual components, and the measurements are
shown in figure 15.
C1
4n
2.17V
R1
2.165V
2.16V
L1
in
input
V1
+
+
V(tantalu m)
2.1495V
V2
2.1490V
C2
R2
+
+
C5
0.36
0
0
0
0.1V
NOJD337K004R
NOJD337K004R
2.1485V
2.1480V
out
90nH
0.01
V(ceramic)
0
5.0V
2.5V
Figure 18: Circuit diagram for simulation of
DC/DC converter output filter
0V
94us
95us
V(input)
V(tantalu m)
96us
V(ce ra mic)
97us
98us
Ti me
3 . 0V
Figure 15: The result of measured ripple voltage
level
2 . 0V
A comparison of the simulation and measurements
shows no significant differences. This proves the
accuracy of the simulation. To a large extent,
measurement can be replaced by simulation to yield
a shorter development cycle.
The last example demonstrates the flexibility of
simulating a real DC/DC converter (Figure 16). An
1 . 0V
0V
0s
V( i n )
5u s
V( o ut )
10 u s
15 us
2 0 us
2 5u s
30 u s
35 us
4 0u s
Ti me
Figure 19: Simulation result voltage transient of
DC/DC converter before and after output passive
filter
SUMMARY
An equivalent circuit diagram for capacitors has
been developed because of the need to include the
non-ideal aspects of a real capacitor’s behavior.
Figure 16: Physical DC/DC converter
actual DC/DC converter was measured and
overloaded to create higher output voltage ripple to
demonstrate that even an overloaded DC/DC
converter can be successfully simulated.
The input and output voltage levels are shown in
graphs of figure 17. The DC/DC converter was
These models for all Tantalum and Niobium Oxide
capacitors have been assembled into a library that
can be incorporated into simulation software.
The library of electronic components for simulation
software is a useful tool for fast, flexible electronic
circuit design and development.
3
Component files from the library can be freely and
widely used for frequency, transient, AC and DC
analysis with real temperature behavior.
Voltage (V)
2.5
2
1.5
1
0.5
0
0
5
10
15
20
25
30
35
40
Time (us)
Figure 17: Measured result of voltage transient
real DC/DC converter before and after output
passive filter
both modeled in the simulation software and
created from real circuit components (Figure 18).
Figure 19 shows the result of the simulation. Here
also the simulation result is identical to the
measurement of the actual device, further proving
the correct functionality of the equivalent circuit
diagrams.
Examples were used to demonstrate the use of
models of a variety of components together with
models of Tantalum and Niobium Oxide capacitors
to efficiently create an accurate circuit simulation.
REFERENCES
[1] J.Sikula et al., Tantalum Capacitor as a MIS
Structure; CARTS USA 2000, 102-106
[2] A.Teverovsky, Reverse Bias Behaviour of
Surface Mount Solid Tantalum Capacitors;
CARTS USA 2002, 105-123
(www.penzar.com)
[3] Penzar’s
TopSPICE
includes real Tantalum and Niobium Oxide
capacitors libraries into simulation software